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A self-developed 6 DOF articulated flexible coordinate measuring machine was introduced in this paper. The parameters of the measuring equation of this machine were identified. A fast, easy calibration method using a special cone socket was proposed. This method was based on the spatial single-point standard provided by the cone socket. The measuring equation of the machine was solved using a non-linear least square computational method, Gauss-Newton method, which can get the values of the parameters. Experimental results showed that this method can effectively improve the over-all accuracy of the flexible measuring machine, and also has the advantages of easy operation and high efficiency.